The plants are found in garden ponds but can block waterways and river banks, and harm wildlife and their habitats if they get out into the wild.
The campaign targets parrot's feather, floating pennywort, water primrose, water fern and New Zealand pigmyweed.
The government said gardeners should be aware of what they are growing in their ponds and dispose of plants carefully.
The problem comes when people clear their garden ponds and dump, or even replant, the species in the wild.
The New Forest in Hampshire and Richmond Park in London have already been affected by the problem.
Some plants can become so thick they make water look like dry land and become a drowning risk to people and animals, ministers said.
TV gardener Charlie Dimmock, who is backing the Be Plant Wise initiative, said enthusiasts must "all play our part in making sure invasive aquatic plants don't cause serious damage to our beautiful waterways".
She advised gardeners to compost the plants they wanted to dispose of, or put them on a lawn where they would be unable to survive.
Natural Environment Minister Huw Irranca-Davies added: "From the River Severn to the smallest stream, our waterways are being invaded.
"We all know about grey squirrels and Japanese knotweed but how many people know that invasive aquatic plants can out-compete native species, choke waterways, harm native wildlife, disrupt the navigation of boats, interfere with recreational activities such as fishing and boating and exacerbate flooding?
"Gardeners can do their bit to help stop the spread by knowing what they grow in their ponds and disposing of unwanted plants with the utmost care."